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Chapter 9
GAS POWER CYCLES
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Thermodynamics: An Engineering Approach Seventh Edition
Yunus A. Cengel, Michael A. Boles
McGraw-Hill, 2011
2
BASIC CONSIDERATIONS IN THE ANALYSIS
OF POWER CYCLES
Modeling is a
powerful
engineering tool
that provides great
insight and
simplicity at the
expense of some
loss in accuracy.
Most power-producing devices operate on cycles.
Ideal cycle: A cycle that resembles the actual cycle
closely but is made up totally of internally reversible
processes.
Reversible cycles such as Carnot cycle have the
highest thermal efficiency of all heat engines
operating between the same temperature levels.
Unlike ideal cycles, they are totally reversible, and
unsuitable as a realistic model.
Thermal efficiency
of heat engines:
The analysis of many complex
processes can be reduced to
a manageable level by
utilizing some idealizations.
3
The ideal cycles are internally reversible, but, unlike the Carnot cycle, they are not
necessarily externally reversible. Therefore, the thermal efficiency of an ideal
cycle, in general, is less than that of a totally reversible cycle operating between
the same temperature limits. However, it is still considerably higher than the
thermal efficiency of an actual cycle because of the idealizations utilized.
4
The idealizations and simplifications in the
analysis of power cycles:
1. The cycle does not involve any friction.
Therefore, the working fluid does not
experience any pressure drop as it flows in
pipes or devices such as heat exchangers.
2. All expansion and compression processes
take place in a quasi-equilibrium manner.
3. The pipes connecting the various
components of a system are well
insulated, and heat transfer through them
is negligible.
Care should be exercised
in the interpretation of the
results from ideal cycles.
On both P-v and T-s diagrams, the area enclosed
by the process curve represents the net work of the
cycle.
On a T-s diagram, the ratio of the
area enclosed by the cyclic curve to
the area under the heat-addition
process curve represents the thermal
efficiency of the cycle. Any
modification that increases the ratio
of these two areas will also increase
the thermal efficiency of the cycle.
5
THE CARNOT CYCLE AND ITS
VALUE IN ENGINEERING
P-v and T-s diagrams of
a Carnot cycle.
The Carnot cycle is composed of four totally reversible
processes: isothermal heat addition, isentropic
expansion, isothermal heat rejection, and isentropic
compression.
For both ideal and actual cycles: Thermal efficiency
increases with an increase in the average temperature
at which heat is supplied to the system or with a
decrease in the average temperature at which heat is
rejected from the system.
A steady-flow Carnot engine.
6
AIR-STANDARD ASSUMPTIONS
The combustion process is replaced by
a heat-addition process in ideal cycles.
Air-standard assumptions:
1. The working fluid is air, which
continuously circulates in a closed loop
and always behaves as an ideal gas.
2. All the processes that make up the
cycle are internally reversible.
3. The combustion process is replaced by
a heat-addition process from an
external source.
4. The exhaust process is replaced by a
heat-rejection process that restores the
working fluid to its initial state.
Cold-air-standard assumptions: When the working fluid is considered
to be air with constant specific heats at room temperature (25°C).
Air-standard cycle: A cycle for which the air-standard assumptions are
applicable.
7
AN OVERVIEW OF RECIPROCATING ENGINES
Nomenclature for reciprocating engines.
• Spark-ignition (SI) engines
• Compression-ignition (CI) engines
Compression ratio
Mean effective
pressure
8
OTTO CYCLE: THE IDEAL CYCLE FOR
SPARK-IGNITION ENGINES
Actual and ideal cycles in spark-ignition engines and their P-v diagrams.
9
Schematic of a two-stroke
reciprocating engine.
The two-stroke engines are
generally less efficient than
their four-stroke counterparts
but they are relatively simple
and inexpensive, and they
have high power-to-weight
and power-to-volume ratios.
T-s diagram
of the ideal
Otto cycle.
Four-stroke cycle
1 cycle = 4 stroke = 2 revolution
Two-stroke cycle
1 cycle = 2 stroke = 1 revolution
10
11
The thermal efficiency of the
Otto cycle increases with the
specific heat ratio k of the
working fluid.
Thermal efficiency of the ideal
Otto cycle as a function of
compression ratio (k = 1.4).
In SI engines,
the
compression
ratio is limited
by
autoignition
or engine
knock.
12
DIESEL CYCLE: THE IDEAL CYCLE
FOR COMPRESSION-IGNITION ENGINES
In diesel engines, the spark plug is replaced
by a fuel injector, and only air is compressed
during the compression process.
In diesel engines, only air is compressed during the
compression stroke, eliminating the possibility of
autoignition (engine knock). Therefore, diesel engines
can be designed to operate at much higher compression
ratios than SI engines, typically between 12 and 24.
1-2 isentropic
compression
2-3 constant-
volume heat
addition
3-4 isentropic
expansion
4-1 constant-
volume heat
rejection.
13
Thermal
efficiency of the
ideal Diesel cycle
as a function of
compression and
cutoff ratios
(k=1.4).
Cutoff
ratio
for the same compression ratio
14
QUESTIONS ???
Diesel engines operate at
higher air-fuel ratios than
gasoline engines. Why?
Despite higher power to
weight ratios, two-stroke
engines are not used in
automobiles. Why?
The stationary diesel
engines are among the
most efficient power
producing devices (about
50%). Why?
What is a turbocharger?
Why are they mostly used
in diesel engines
compared to gasoline
engines.
P-v diagram of an ideal dual cycle.
Dual cycle: A more realistic
ideal cycle model for modern,
high-speed compression ignition
engine.
15
STIRLING AND ERICSSON CYCLES
A regenerator is a device that
borrows energy from the working
fluid during one part of the cycle
and pays it back (without
interest) during another part.
Stirling cycle 1-2 T = constant expansion (heat addition from the external source)
2-3 v = constant regeneration (internal heat transfer from the working fluid to the regenerator)
3-4 T = constant compression (heat rejection to the external sink)
4-1 v = constant regeneration (internal heat transfer from the regenerator back to the working
fluid)
T-s and P- vdiagrams of Carnot, Stirling, and Ericsson cycles.
16
The execution of the Stirling cycle. A steady-flow Ericsson engine.
The Ericsson cycle is very much like the
Stirling cycle, except that the two constant-
volume processes are replaced by two
constant-pressure processes.
Both the Stirling and Ericsson cycles are
totally reversible, as is the Carnot cycle,
and thus:
The Stirling and Ericsson cycles
give a message: Regeneration
can increase efficiency.
17
BRAYTON CYCLE: THE IDEAL CYCLE
FOR GAS-TURBINE ENGINES
An open-cycle gas-turbine engine. A closed-cycle gas-turbine engine.
The combustion process is replaced by a constant-pressure heat-addition
process from an external source, and the exhaust process is replaced by a
constant-pressure heat-rejection process to the ambient air.
1-2 Isentropic compression (in a compressor)
2-3 Constant-pressure heat addition
3-4 Isentropic expansion (in a turbine)
4-1 Constant-pressure heat rejection
18
T-s and P-v diagrams for
the ideal Brayton cycle.
Pressure
ratio
Thermal
efficiency of the
ideal Brayton
cycle as a
function of the
pressure ratio.
19
The fraction of the turbine work
used to drive the compressor is
called the back work ratio.
The two major application areas of gas-
turbine engines are aircraft propulsion
and electric power generation.
The highest temperature in the cycle is
limited by the maximum temperature that
the turbine blades can withstand. This
also limits the pressure ratios that can be
used in the cycle.
The air in gas turbines supplies the
necessary oxidant for the combustion of
the fuel, and it serves as a coolant to
keep the temperature of various
components within safe limits. An air–fuel
ratio of 50 or above is not uncommon.
20
Development of Gas Turbines
1. Increasing the turbine inlet (or firing) temperatures
2. Increasing the efficiencies of turbomachinery components (turbines,
compressors):
3. Adding modifications to the basic cycle (intercooling, regeneration or
recuperation, and reheating).
Deviation of Actual Gas-
Turbine Cycles from Idealized
Ones
The deviation of an actual gas-
turbine cycle from the ideal
Brayton cycle as a result of
irreversibilities.
Reasons: Irreversibilities in turbine and
compressors, pressure drops, heat losses
Isentropic efficiencies of the compressor
and turbine
21
THE BRAYTON CYCLE WITH
REGENERATION In gas-turbine engines, the temperature of the exhaust
gas leaving the turbine is often considerably higher than
the temperature of the air leaving the compressor.
Therefore, the high-pressure air leaving the compressor
can be heated by the hot exhaust gases in a counter-flow
heat exchanger (a regenerator or a recuperator).
The thermal efficiency of the Brayton cycle increases as a
result of regeneration since less fuel is used for the same
work output.
T-s diagram of a
Brayton cycle with
regeneration.
A gas-turbine
engine with
regenerator.
22
T-s diagram of a Brayton
cycle with regeneration.
Effectiveness
of regenerator
Effectiveness under cold-
air standard assumptions
Under cold-air
standard assumptions
Thermal
efficiency of the
ideal Brayton
cycle with and
without
regeneration.
The thermal efficiency depends on the ratio of the minimum to maximum temperatures as well as the pressure ratio.
Regeneration is most effective at lower pressure ratios and low minimum-to-maximum temperature ratios.
Can regeneration
be used at high
pressure ratios?
23
THE BRAYTON CYCLE WITH INTERCOOLING,
REHEATING, AND REGENERATION
A gas-turbine engine
with two-stage
compression with
intercooling, two-
stage expansion
with reheating, and
regeneration and its
T-s diagram.
For minimizing work input to compressor
and maximizing work output from turbine:
24
Comparison
of work inputs
to a single-
stage
compressor
(1AC) and a
two-stage
compressor
with
intercooling
(1ABD).
Multistage compression with intercooling: The work required to compress a gas
between two specified pressures can be decreased by carrying out the compression
process in stages and cooling the gas in between. This keeps the specific volume as low
as possible.
Multistage expansion with reheating keeps the specific volume of the working fluid as
high as possible during an expansion process, thus maximizing work output.
Intercooling and reheating always decreases the thermal efficiency unless they are
accompanied by regeneration. Why?
As the number of compression and expansion
stages increases, the gas-turbine cycle with
intercooling, reheating, and regeneration
approaches the Ericsson cycle.
25
IDEAL JET-PROPULSION CYCLES
In jet engines, the high-
temperature and high-
pressure gases leaving the
turbine are accelerated in a
nozzle to provide thrust.
Gas-turbine engines are widely used to power aircraft because they are light and
compact and have a high power-to-weight ratio.
Aircraft gas turbines operate on an open cycle called a jet-propulsion cycle.
The ideal jet-propulsion cycle differs from the simple ideal Brayton cycle in that the
gases are not expanded to the ambient pressure in the turbine. Instead, they are
expanded to a pressure such that the power produced by the turbine is just sufficient to
drive the compressor and the auxiliary equipment.
The net work output of a jet-propulsion cycle is zero. The gases that exit the turbine at a
relatively high pressure are subsequently accelerated in a nozzle to provide the thrust to
propel the aircraft.
Aircraft are propelled by accelerating a fluid in the opposite direction to motion. This is
accomplished by either slightly accelerating a large mass of fluid (propeller-driven
engine) or greatly accelerating a small mass of fluid (jet or turbojet engine) or both
(turboprop engine).
26
Basic components of a turbojet engine and the T-s diagram for the ideal turbojet cycle.
Propulsive power is
the thrust acting on the
aircraft through a
distance per unit time.
Propulsive efficiency
Propulsive power
Thrust (propulsive force)
27
28
Modifications to Turbojet Engines
The first airplanes built were all propeller-driven, with propellers powered by
engines essentially identical to automobile engines.
Both propeller-driven engines and jet-propulsion-driven engines have their own
strengths and limitations, and several attempts have been made to combine the
desirable characteristics of both in one engine.
Two such modifications are the propjet engine and the turbofan engine.
The most widely used engine in aircraft propulsion is the turbofan (or fanjet)
engine wherein a large fan driven by the turbine forces a considerable
amount of air through a duct (cowl) surrounding the engine.
A
turbofan
engine.
29
30
A turboprop
engine.
A ramjet
engine.
Various engine types:
Turbofan, Propjet, Ramjet, Sacramjet, Rocket
31
SECOND-LAW ANALYSIS OF GAS POWER CYCLES
Exergy
destruction for a
closed system
For a steady-
flow system
Steady-flow, one-inlet, one-exit
Exergy destruction of a cycle
For a cycle with heat transfer
only with a source and a sink
Closed system exergy
Stream exergy
A second-law analysis of these cycles reveals where the largest
irreversibilities occur and where to start improvements.
32
Example 1: An ideal Otto cycle has a compression ratio of 8. At the beginning of the
compression process, air is at 100 kPa and 17°C, and 800 kJ/kg of heat is transferred to
air during the constant-volume heat-addition process. Accounting for the variation of
specific heats of air with temperature, determine (a) the maximum temperature and
pressure that occur during the cycle, (b) the net work output, (c) the thermal efficiency,
and (d ) the mean effective pressure for the cycle.
33
34
35
36
Example 2: A gas-turbine power plant operating on an ideal Brayton cycle has a
pressure ratio of 8. The gas temperature is 300 K at the compressor inlet and 1300 K
at the turbine inlet. Utilizing the air-standard assumptions, determine (a) the gas
temperature at the exits of the compressor and the turbine, (b) the back work ratio, and
(c) the thermal efficiency.
37
38
39
Example 3: An ideal gas-turbine cycle with two stages of compression and two stages
of expansion has an overall pressure ratio of 8. Air enters each stage of the compressor
at 300 K and each stage of the turbine at 1300 K. Determine the back work ratio and the
thermal efficiency of this gas-turbine cycle, assuming (a) no regenerators and (b) an
ideal regenerator with 100 percent effectiveness.
40
41
42